Approaches for Constrained Parametric Curve Interpolation

The construction of a GC^1 cubic interpolating curve that lieson the same side of a given straight line as the data points is studied.The main task is to choose appropriate approaches to modify tangentvectors at the data points for the desired curve. Three types ofapproaches for changing the magnitudes of the tangent vectors arepresented. The first-type approach modifies the tangent vectors byapplying a constraint to the curve segment. The second one does the workby optimization techniques. The third one is a modification of theexisting method. Three criteria are presented to compare the three typesof approaches with the existing method. The experiments that test theeffectiveness of the approaches are included.